Human Perception of the Statistical Properties of Discrete Time Series: Effects of Interpolation Methods

The human´s ability to estimate the mean and standard deviation of discrete time series is discussed. The effect of polynomial interpolation formulas on these two statistics is considered both mathematically and experimentally. Derivations show that the piece-wise continuous functions resulting from polynomial interpolation have unbiased expected values and biased variances. Results of two experiments are presented that support the idea that humans base their perceptions on the piece-wise continuous result of interpolation and thereby transmit the statistical bias. The practical implications of these results are discussed.